Miller-Orr Cash Management Model

## Miller-Orr Cash Management Model

### Core Idea

When cash flows are uncertain and stochastic (random), Baumol's deterministic model breaks down. The Miller-Orr model applies control theory to such random cash flows.

It is a control-limit model that determines the timing and size of transfers between an investment account and a cash account.

### The Three Limits

```

Cash Balance

|

H |-------- Upper Control Limit

|

|

Z |-------- Return Point

|

|

0 |-------- Lower Control Limit

```

• h (Upper Limit): Cash ceiling
• z (Return Point): Target cash balance after a transaction
• 0 (Lower Limit): Cash floor

### How the Model Works

1. When cash balance hits 'h' (upper limit):

• Transfer (h − z) to marketable securities.
• Cash drops back to z.

2. When cash balance hits '0' (lower limit):

• Liquidate marketable securities equal to z and move to cash.
• Cash rises back to z.

3. When cash stays between 0 and h (in the bands (0, z) and (z, h)):

• No transactions are made.
• Cash fluctuates randomly.

### How the Limits Are Set

The high and low limits depend on:

• Fixed cost per securities transaction
• Opportunity cost of holding cash (interest forgone)
• Degree of likely fluctuations in cash balances (variance)

These limits are designed to satisfy cash demands at the lowest possible total cost.

### Why Miller-Orr Over Baumol